The reduction of acid gas emissions such as industrial CO2 has become a major challenge for the environment, and therefore for many industrialists. One solution for reducing these emissions is based on the geologic sequestration of these gases. The principle consists in capturing the CO2 at the emission point thereof (power plant, cement plant, steelworks . . . ), in concentrating it and in transporting it to a suitable geologic site for storage. Technologies for capturing and storing CO2 are already available. This option has been widely studied for some years at the international level, especially by the petroleum industries that see a second advantage therein: the development of the geologic storage of carbon dioxide by injecting CO2 in support to an enhanced oil recovery (EOR) operation or enhanced natural gas recovery in unworkable coal veins (ECBM; Enhanced Coalbed Methane) and in natural gas reservoirs (EGR; Enhanced Gas Recovery). In this context, the option considered for CO2 storage is the use of natural underground reservoirs (depleted oil and gas reservoirs, unworkable coal fields, saline aquifers and saline cavities). This type of embodiment is illustrated in FIG. 1, where a producing well (PROD) extracts hydrocarbons from the subsurface while an injection well (INJ) re-injects CO2 into the reservoir.
The cost linked with the development of a storage site being high, the economic challenges and the environmental impacts being also great, it is necessary, in order to develop such acid gas storage methods in natural geologic reservoirs, to perfectly determine the long-term storage conditions. This mainly consists in studying migration of the gas within the reservoir and the precipitation and dissolution reactions to determine the quality of a storage site in the course of time.
A technical solution to this long-term storage site evaluation problem is provided by techniques allowing geochemical systems to be modelled.
The following documents that are mentioned in the description hereafter illustrate the prior art:
[1] G. T. Yeh and V. S. Tripathi “A Critical Evaluation of Recent Developments in Hydrogeochemical Transport Models of Reactive Multichemical Components”, Water Resources Research, Vol. 25. No. 1, 93-108, January 1989,
[2] Y. Le Gallo, O. Bildstein and E. Brosse “Coupled reaction-flow modeling of diagenetic changes in reservoir permeability, porosity and mineral composition.”, Journal of Hydrology 209 (1-4), 366-388, August 1998,
[3] J. W. Johnson, J. J. Nitao, C. I. Steefel, K. G. Knauss “Reactive transport modelling of CO2 storage in saline aquifers to elucidate fundamental processes, trapping mechanisms, and sequestration partitioning”, GS-London Spec. Pub. ms, Aug. 8, 2002,
[4] Long Nghiem, Peter Sammon, Jim Grabenstetter and Hiroshi Ohkuma, “Modeling CO2 Storage in Aquifers with a Fully-Coupled Geochemical EOS Compositional Simulator”, SPE 89474, April 2004,
[5] Tianfu Xu and K. Pruess “Modeling multiphase no-isothermal fluid flow and reactive geochemical transport in variably saturated fractured rocks: 1. Methodology”, American Journal of Science, Vol. 301, P. 16-33, January 2001,
[6] Hui Cao “Development of techniques for general purpose simulators”, PhD Stanford University, June 2002,
[7] Jacob Bear “Dynamics of Fluids in Porous Media”, American Elsevier, 1972. Reprinted with corrections, Dover, N.Y., 1988.
The past thirty years, there has been a large increase in the number of methods allowing geochemical systems, whether natural or induced, to be modelled. What is referred to as geochemical system is a porous medium such as a rock volume wherein at least an aqueous phase and possibly a gas phase circulate. These systems are characterized by two types of processes:                a fluid transport process,        a process of chemical reactions between the various elements that are the medium and the aqueous and gas phases: rock/water and water/gas for example.        
Precise modelling of these geochemical systems allows for example to determine the acid gas trapping mechanisms in geologic formations. Such a modelling also allows to determine the soil depollution conditions using multiphase processes.
The models used must be representative of the behaviour of these geochemical systems. Such models are based on the mass conservation principle: the mass is neither created nor destroyed in the system, but transferred between the solid, the aqueous phase and the gas phase. There are two types of models:                the models that do not take account of transport processes. These models are referred to as “chemical reaction models” or simply “batch models”;        the models that consider both the transport and the chemical reaction processes are called “reactive transport model”. One then refers to coupled modelling.        
Definition of such models is complex and their use can be limited by computer capacities and/or by the computing time that increases considerably depending on the number of constituents to be considered. The chemical constituents, such as CO2, H2O or NaCl for example, can be present either in the gas phase or in the water phase.
Geochemical system models were first used to understand the basic phenomena linked with water chemistry or with the evolution of diagenetic processes (see [2]). For about ten years, models were directed towards the analysis of the environmental impact of soil pollution, of biogas emissions in dumps or the study of radioactive waste storage (see [3] [4]). Finally, their use was recently extended to the study of acid gas (H2S, CO2, CH4) geologic storage.
A reactive transport model allows to simulate the hydrodynamic processes leading to migration and dispersion of constituents (transport) linked with geochemical processes (chemical reactions). Initially used to solve hydrogeologic systems (see [2]), reactive transport models are increasingly used to simulate CO2 injection, migration and storage in geologic layers (see [3] [4]). Introduction of a constituent initially present in gaseous form (CO2) requires to consider models that are no longer single-phase models (water only), but two-phase models (water-gas), and therefore to increase the number of unknowns of the model.
From a general point of view, a reactive transport model is a method allowing to find the solution to a system of equations of the type as follows:
                                          ∂                          (                              ϕ                ·                                  C                  i                                            )                                            ∂            t                          =                              L            ⁡                          (                              c                i                            )                                +                      R            ⁡                          (                              C                i                            )                                                          (        1        )            where φ is the porosity of the medium, ci the concentration of constituent i in the mobile phases (fluids) and Ci the total concentration (fluids+rock). We thus have the relation: Ci=ci+ ci where ci is the “motionless” phase (concentration in the motionless phase: the rock). L(ci) defines the transport operator of constituent i and R(Ci) the chemical reaction operator.
System (1) is difficult to solve because of the large number of unknowns and of the great non-linearities induced by the reaction terms. Today there are essentially two approaches for solving such systems:
1. an iterative sequential solution method;
2. a simultaneous solution method.
Each one of these approaches can be solved explicitly or implicitly. A solution is referred to as explicit when one seeks the solution to a temporal system with t+dt by means of state t.
The first one, the iterative sequential solution method, is the most commonly used for solving this type of problem (see [2]). It consists in solving the system of equations in two stages: a transport stage without reaction and a stage of chemical reactions cell by cell (during the same time interval). Yeh and Tripathi have shown (see [1]) that an iterative loop has to be added to be able to sufficiently minimize the numerical errors on mass conservation. This sequential solution method was developed and analyzed for 2D or 3D water single-phase reactive flow modelling in porous media. It has been lately extended to the modelling of multiphase problems by Xu et al. (see [5]).
The second one, the simultaneous solution method, solves the complete system in a single stage. This method allows to solve complex geochemical systems and it is theoretically very robust. In practice, as shown by Yeh and Tripathi in a reference paper (see [1]), it can quickly become costly in CPU time and in memory space for complex systems. The models developed from these approaches were till now reserved for water single-phase flows. Recent studies such as Nghiem et al.'s (see [4]) show that such an approach can now be considered for 3D compositional multiphase problems, but with a limited number of constituents, which is not precise enough to allow an application within the context of acid gas storage capacity evaluation.
The method according to the invention turns to good account the advantages of the sequential methods (local time intervals, parallelization, reduced memory size) while avoiding addition of another iterative loop. It thus meets the requirements linked with the evaluation of the acid gas (H2S, CO2, CH4) storage capacities of an underground medium representing a complex multiphase geochemical system.